Orthogonal Matrices: Rotation & Reflection

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Orthogonal matrices have determinants of either +1 or -1, indicating the type of transformation they represent. A determinant of +1 corresponds to a rotation, while a determinant of -1 indicates a reflection across one or more axes. The discussion seeks clarification on these properties, particularly in three-dimensional space. Additionally, it mentions the relevance of cubic polynomials having real roots in understanding these transformations. Understanding these concepts is crucial for grasping the geometric implications of orthogonal matrices.
neelakash
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We know that if M is an orthogonal matrix,then DetM=(+-)1
When Det M=1,thee transformation is a rotation.And for reflection about anyone o all three axes DetM=-1.
I did this..
But I did not know that information:When Det M=1,thee transformation is a rotation.And for reflection about anyone o all three axes DetM=-1.

Can anyone please justify this...
or give any link that can clarify the matter?
 
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try dimwension three. and recall a cubic polynomila has a real root.
 

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